PARAMETER IDENTIFICATION PROBLEMS FOR A CLASS OF STRONGLY DAMPED NONLINEAR WAVE EQUATIONS

Abstract

Parameter identification problems of spatially varying coefficients in a class of strongly damped nonlinear wave equations are studied. The problems are formulated by a minimization of quadratic cost functionals by means of distributive and terminal values measurements. The existence of optimal parameters and necessary optimality conditions for the functionals are proved by the continuity and Gˆateaux differentiability of solutions on parameters.